As the meshes are not uniform in any net, the tensions on their arms cannot be equal to each other, though the net is stretched as uniformly as possible. To know the actual value of the dispersion of tension caused by the irregularity of meshes, the author has studied Pearson's coefficient of variation
V with cotton nets.
In the net, spread uniformly on a vertical rectangular iron frame 1.5m high and 1.0m broad, and loaded uniformly on its bottom with some wèights (40.-80.kg), the tension on each arm is measured one by one with an apparatus as shown in Fig. 1. The measurement with this apparatus is affected by the inaccuracy due to the construction of the latter, and moreover gives too small values of the tension when the arm runs as (1) in Fig. 2, and too large ones when it runs as (2). The tention, being affected by the friction at the vertical edges of the frame, varies systematically from the top to the bottom with the step of the meshés. Deducting the variances caused by the various hindrances like that, the author has got the following relation:
(
V/100)
2=
σ12+
σ22/2
m2(1-
r2)-(
v/100)
2,
where
σ1,
σ2 are the standard deviations of the tension calculated seperately with the cords running as (1) and with those running as (2),
m is the arithmetic mean of the ten ?? ion,
r is the correlatian ceofficient between the tension and the step of meshes, and
v is the coefficient of variation in per cent which is due to the errors of observation. Considering both the sampling error and the error of
v2,
σv=1/4
V√2
V4/
N{1+2(
V/100)
2}+
σ2v2,
where
N is the number of arms observed.
The result of calculation, which is tabulated in Tab. 1, indicates that the values of
V do not differ from each other among the nets having knots of the same kind, and the weighted mean of
V is, as in Tab. 2,
8.4±0.19 (standard error) for the net of trawl knots,
and 5.6±0.21 ( ?? ) for the net of flat knots.
View full abstract